Difference between revisions of "Power set"

Revision as of 07:43, 23 August 2015 (view source) JessicaBelinda133 (Talk | contribs) ← Older edit		Latest revision as of 16:30, 23 August 2015 (view source) Alec (Talk | contribs) m (Reverted edits by JessicaBelinda133 (talk) to last revision by Alec)
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−	The power set of a a mighty set that fights against all that approachs it	+	The power set of a set <math>X</math> is denoted by <math>\mathcal{P}(X)</math>, sometimes <math>2^X</math> (a number to the power of a set is not defined (as it cannot be usefully defined) leaving it free to be used as notation. This comes from the [[Cardinality|cardinality]] of the power set being <math>2^{|X|}</math>)
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		+	The characteristic property of the power set is that <math>\forall U\subset X:U\in\mathcal{P}(X)</math>
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		+	It is the set of all subsets of <math>X</math>
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		+	{{Definition}}

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Latest revision as of 16:30, 23 August 2015

The power set of a set

$$X$$ is denoted by $$\mathcal{P}(X)$$ , sometimes $$2^X$$ (a number to the power of a set is not defined (as it cannot be usefully defined) leaving it free to be used as notation. This comes from the cardinality of the power set being $$2^{|X|}$$ )

The characteristic property of the power set is that

$$\forall U\subset X:U\in\mathcal{P}(X)$$

It is the set of all subsets of

$$X$$